Tuesday, July 2, 2013

Understanding the Concept of Inequalities

In mathematics there is system of linear equations. The equations are formed when there is an ‘equal to’ symbol present in the given expression. If the ‘equal to’ symbol is replaced by a ‘greater than’ or ‘lesser than’ symbol the equation becomes an inequality. When a set of equations are given it forms a system of equations. The equations can be linear in nature and also quadratic in nature. Equations of higher degrees are also present. The higher the degree of the equation the more complex the equation becomes. It is difficult and also time consuming to solve the equations of higher degrees. But the linear equations can be easily solved. The simple concept of transposing is used in solving them. There are both variables and constants present in an equation. The value of constants does not change throughout the equation but the value of the variables changes. The variables can assume various values.

Just like the system of equations there is also the system of inequalities in mathematics. The method of solving them is similar to the system of equations. But the ‘greater than’ or ‘lesser than’ inequality must be kept in mind before solving them, otherwise the whole answer can go wrong. The inequality can also be treated as a constraint. The final solution must satisfy this inequality or constraint. If the solution does not do so then it is not the correct answer. The solution must be found out again and must be checked for its feasibility. The systems of inequalities can be easily solved just like the system of equations.

The art of solving systems of inequalities can be easily learnt if one is thorough with the concept of solving the system of linear equations. The difference between the two is only in the symbols used. The graphical method can also be used to solve the same. The graphical method is a pictorial method of finding the solution to this method. The equation or the inequality given in the question is plotted on the graph and the solution is found accordingly. It is an easy method of understanding the concept. Once the solution is obtained through this method it is very easy to check its feasibility. The feasibility of the solution can be understood by looking at the graph itself. Once the solutions that are obtained are found to be feasible they must be accepted as the solutions.